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Read in the following dictionary:
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 x_{8}   &  -3.0 & +  5.00 x_{1} & -6.00 x_{2} & -8.00 x_{3} & -10.00 x_{4} & +  6.00 x_{5} & -6.00 x_{6} & -6.00 x_{7}\\
 x_{9}   &  -3.0 & +  4.00 x_{1} & +  2.00 x_{2} & -3.00 x_{3} &   & +  3.00 x_{5} & +  1.00 x_{6} & +  9.00 x_{7}\\
 x_{10}   &  3.0 & +  5.00 x_{1} & -3.00 x_{2} & +  8.00 x_{3} & +  4.00 x_{4} & +  8.00 x_{5} & -6.00 x_{6} & +  3.00 x_{7}\\
 x_{11}   &  1.0 & +  2.00 x_{1} & +  6.00 x_{2} & +  2.00 x_{3} & -5.00 x_{4} & -1.00 x_{5} &    &   \\
 x_{12}   &  -2.0 & + 10.00 x_{1} & -4.00 x_{2} & +  9.00 x_{3} & +  2.00 x_{4} & -6.00 x_{5} & +  4.00 x_{6} & -1.00 x_{7}\\
 x_{13}   &  -2.0 & -7.00 x_{1} & -8.00 x_{2} & -6.00 x_{3} & -8.00 x_{4} & -7.00 x_{5} & +  1.00 x_{6} & +  3.00 x_{7}\\
 x_{14}   &  3.0 & -6.00 x_{1} & +  8.00 x_{2} & +  6.00 x_{3} & +  5.00 x_{4} & +  7.00 x_{5} & +  3.00 x_{6} & -8.00 x_{7}\\
\hline
z    &  0.0 & -4.00 x_{1} &   & -5.00 x_{3} & -3.00 x_{4} & +  4.00 x_{5} & -1.00 x_{6} & +  5.00 x_{7}\\
\end{array}\]
\subsection{Initialization Phase: Dual Problem Solving}
New Objective in primal was changed to : \[ \max\ \sum_{j=1}^{7}\ - x_j \] 
Primal variable $x_j$ corresponds to dual variable $y_j$ for $j = 1,\ldots,14$
Dual Dictionary (with objective changed is): 
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{1}   &  1.0 & -5.00 y_{8} & -4.00 y_{9} & -5.00 y_{10} & -2.00 y_{11} & -10.00 y_{12} & +  7.00 y_{13} & +  6.00 y_{14}\\
 y_{2}   &  1.0 & +  6.00 y_{8} & -2.00 y_{9} & +  3.00 y_{10} & -6.00 y_{11} & +  4.00 y_{12} & +  8.00 y_{13} & -8.00 y_{14}\\
 y_{3}   &  1.0 & +  8.00 y_{8} & +  3.00 y_{9} & -8.00 y_{10} & -2.00 y_{11} & -9.00 y_{12} & +  6.00 y_{13} & -6.00 y_{14}\\
 y_{4}   &  1.0 & + 10.00 y_{8} &   & -4.00 y_{10} & +  5.00 y_{11} & -2.00 y_{12} & +  8.00 y_{13} & -5.00 y_{14}\\
 y_{5}   &  1.0 & -6.00 y_{8} & -3.00 y_{9} & -8.00 y_{10} & +  1.00 y_{11} & +  6.00 y_{12} & +  7.00 y_{13} & -7.00 y_{14}\\
 y_{6}   &  1.0 & +  6.00 y_{8} & -1.00 y_{9} & +  6.00 y_{10} &   & -4.00 y_{12} & -1.00 y_{13} & -3.00 y_{14}\\
 y_{7}   &  1.0 & +  6.00 y_{8} & -9.00 y_{9} & -3.00 y_{10} &   & +  1.00 y_{12} & -3.00 y_{13} & +  8.00 y_{14}\\
\hline
z    &  -0 & +  3.00 y_{8} & +  3.00 y_{9} & -3.00 y_{10} & -1.00 y_{11} & +  2.00 y_{12} & +  2.00 y_{13} & -3.00 y_{14}\\
\end{array}\]
Unbounded Dictionary!
Initialization returns unbounded dual dictionary after 5 pivots
\[\begin{array}{c| c c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} c@{\hskip 2pt} }
 y_{9}   &  0.208333333333 & -0.15 y_{7} & +  0.50 y_{1} & -2.44 y_{10} & +  1.56 y_{11} & +  8.52 y_{12} & -0.56 y_{5} & -5.77 y_{14}\\
 y_{2}   &  2.83333333333 & -2.08 y_{7} & + 20.00 y_{1} & -61.25 y_{10} & + 53.75 y_{11} & + 324.58 y_{12} & -19.75 y_{5} & -249.58 y_{14}\\
 y_{3}   &  4.04166666667 & -2.73 y_{7} & + 22.50 y_{1} & -86.19 y_{10} & + 65.81 y_{11} & + 355.60 y_{12} & -22.81 y_{5} & -278.85 y_{14}\\
 y_{4}   &  4.08333333333 & -2.96 y_{7} & + 27.00 y_{1} & -94.88 y_{10} & + 86.13 y_{11} & + 433.71 y_{12} & -27.13 y_{5} & -333.21 y_{14}\\
 y_{8}   &  0.208333333333 & -0.15 y_{7} & +  1.50 y_{1} & -5.44 y_{10} & +  4.56 y_{11} & + 24.52 y_{12} & -1.56 y_{5} & -18.77 y_{14}\\
 y_{6}   &  1.91666666667 & -0.54 y_{7} & +  7.00 y_{1} & -19.63 y_{10} & + 21.38 y_{11} & + 110.79 y_{12} & -7.38 y_{5} & -92.29 y_{14}\\
 y_{13}   &  0.125 & -0.19 y_{7} & +  1.50 y_{1} & -4.56 y_{10} & +  4.44 y_{11} & + 23.81 y_{12} & -1.44 y_{5} & -17.56 y_{14}\\
\hline
z    &  1.5 & -1.25 y_{7} & +  9.00 y_{1} & -35.75 y_{10} & + 26.25 y_{11} & + 148.75 y_{12} & -9.25 y_{5} & -111.75 y_{14}\\
\end{array}\]
Original Problem is Infeasible
Infeasible Problem.. Early Exit
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